{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NkfHUS813zJk"
      },
      "source": [
        "##### Copyright 2018 The TensorFlow Probability Authors.\n",
        "\n",
        "Licensed under the Apache License, Version 2.0 (the \"License\");\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "cellView": "form",
        "id": "JC-lgcjL3892"
      },
      "outputs": [],
      "source": [
        "#@title Licensed under the Apache License, Version 2.0 (the \"License\"); { display-mode: \"form\" }\n",
        "# you may not use this file except in compliance with the License.\n",
        "# You may obtain a copy of the License at\n",
        "#\n",
        "# https://www.apache.org/licenses/LICENSE-2.0\n",
        "#\n",
        "# Unless required by applicable law or agreed to in writing, software\n",
        "# distributed under the License is distributed on an \"AS IS\" BASIS,\n",
        "# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
        "# See the License for the specific language governing permissions and\n",
        "# limitations under the License."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Um6EsGjz4RON"
      },
      "source": [
        "# Fitting Dirichlet Process Mixture Model Using Preconditioned Stochastic Gradient Langevin Dynamics\n",
        "<table class=\"tfo-notebook-buttons\" align=\"left\">\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://www.tensorflow.org/probability/examples/Fitting_DPMM_Using_pSGLD\"><img src=\"https://www.tensorflow.org/images/tf_logo_32px.png\" />View on TensorFlow.org</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://colab.research.google.com/github/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/Fitting_DPMM_Using_pSGLD.ipynb\"><img src=\"https://www.tensorflow.org/images/colab_logo_32px.png\" />Run in Google Colab</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a target=\"_blank\" href=\"https://github.com/tensorflow/probability/blob/main/tensorflow_probability/examples/jupyter_notebooks/Fitting_DPMM_Using_pSGLD.ipynb\"><img src=\"https://www.tensorflow.org/images/GitHub-Mark-32px.png\" />View source on GitHub</a>\n",
        "  </td>\n",
        "  <td>\n",
        "    <a href=\"https://storage.googleapis.com/tensorflow_docs/probability/tensorflow_probability/examples/jupyter_notebooks/Fitting_DPMM_Using_pSGLD.ipynb\"><img src=\"https://www.tensorflow.org/images/download_logo_32px.png\" />Download notebook</a>\n",
        "  </td>\n",
        "</table>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vsGdTAPr2FtM"
      },
      "source": [
        "In this notebook, we will demonstrate how to cluster a large number of samples and infer the number of clusters simultaneously by fitting a Dirichlet Process Mixture of Gaussian distribution. We use Preconditioned Stochastic Gradient Langevin Dynamics (pSGLD) for inference. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JcP6n6aWLXUD"
      },
      "source": [
        "## Table of contents"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "S_BcwM7uLoNI"
      },
      "source": [
        "1. Samples\n",
        "\n",
        "1. Model\n",
        "\n",
        "1. Optimization\n",
        "\n",
        "1. Visualize the result\n",
        "\n",
        "  4.1. Clustered result\n",
        "\n",
        "  4.2. Visualize uncertainty\n",
        "  \n",
        "  4.3. Mean and scale of selected mixture component\n",
        "  \n",
        "  4.4. Mixture weight of each mixture component\n",
        "  \n",
        "  4.5. Convergence of $\\alpha$\n",
        "  \n",
        "  4.6. Inferred number of clusters over iterations\n",
        "  \n",
        "  4.7. Fitting the model using RMSProp\n",
        "\n",
        "1. Conclusion"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MMWZGfjzPVaY"
      },
      "source": [
        "---\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "A7RysXxCBNS_"
      },
      "source": [
        "## 1. Samples"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k-aVH4b4Bxzo"
      },
      "source": [
        "First, we set up a toy dataset. We generate 50,000 random samples from three bivariate Gaussian distributions."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "TNGwb4TdrlJO"
      },
      "outputs": [],
      "source": [
        "import time\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import tensorflow.compat.v1 as tf\n",
        "import tensorflow_probability as tfp"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "r5w5P1ZfQjk4"
      },
      "outputs": [],
      "source": [
        "plt.style.use('ggplot')\n",
        "tfd = tfp.distributions"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-KdQXvGgrqVk"
      },
      "outputs": [],
      "source": [
        "def session_options(enable_gpu_ram_resizing=True):\n",
        "  \"\"\"Convenience function which sets common `tf.Session` options.\"\"\"\n",
        "  config = tf.ConfigProto()\n",
        "  config.log_device_placement = True\n",
        "  if enable_gpu_ram_resizing:\n",
        "    # `allow_growth=True` makes it possible to connect multiple colabs to your\n",
        "    # GPU. Otherwise the colab malloc's all GPU ram.\n",
        "    config.gpu_options.allow_growth = True\n",
        "  return config\n",
        "\n",
        "def reset_sess(config=None):\n",
        "  \"\"\"Convenience function to create the TF graph and session, or reset them.\"\"\"\n",
        "  if config is None:\n",
        "    config = session_options()\n",
        "  tf.reset_default_graph()\n",
        "  global sess\n",
        "  try:\n",
        "    sess.close()\n",
        "  except:\n",
        "    pass\n",
        "  sess = tf.InteractiveSession(config=config)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ud3XnrsmCHrb"
      },
      "outputs": [],
      "source": [
        "# For reproducibility\n",
        "rng = np.random.RandomState(seed=45)\n",
        "tf.set_random_seed(76)\n",
        "\n",
        "# Precision\n",
        "dtype = np.float64\n",
        "\n",
        "# Number of training samples\n",
        "num_samples = 50000\n",
        "\n",
        "# Ground truth loc values which we will infer later on. The scale is 1.\n",
        "true_loc = np.array([[-4, -4],\n",
        "                     [0, 0],\n",
        "                     [4, 4]], dtype)\n",
        "\n",
        "true_components_num, dims = true_loc.shape\n",
        "\n",
        "# Generate training samples from ground truth loc\n",
        "true_hidden_component = rng.randint(0, true_components_num, num_samples)\n",
        "observations = (true_loc[true_hidden_component]\n",
        "                + rng.randn(num_samples, dims).astype(dtype))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "BDlv6eGUCJ6u"
      },
      "outputs": [
        {
          "data": {
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nwz0/l/U+fg8yh8t9dDR2Kyber9RsTdkXjcUH/kNjfO4Gw1XIZW3G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wtIYqu6xAlz2M84iWflUE2t8rI5py0GJzPva4TW3cw3yJIEp8HTR2+M0hIcnYBbVq1D62sBZzdd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\nAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 576x396 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Visualize samples\n",
        "plt.scatter(observations[:, 0], observations[:, 1], 1)\n",
        "plt.axis([-10, 10, -10, 10])\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oF2Bft6nNeIw"
      },
      "source": [
        "## 2. Model"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lxeYFFY8Nyrc"
      },
      "source": [
        "Here, we define a Dirichlet Process Mixture of Gaussian distribution with Symmetric Dirichlet Prior. Throughout the notebook, vector quantities are written in bold. Over  $i\\in\\{1,\\ldots,N\\}$ samples, the model with a mixture of $j \\in\\{1,\\ldots,K\\}$ Gaussian distributions is formulated as follow:\n",
        "\n",
        "$$\\begin{align*}\n",
        "p(\\boldsymbol{x}_1,\\cdots, \\boldsymbol{x}_N) &=\\prod_{i=1}^N \\text{GMM}(x_i), \\\\\n",
        "&\\,\\quad \\text{with}\\;\\text{GMM}(x_i)=\\sum_{j=1}^K\\pi_j\\text{Normal}(x_i\\,|\\,\\text{loc}=\\boldsymbol{\\mu_{j}},\\,\\text{scale}=\\boldsymbol{\\sigma_{j}})\\\\ \n",
        "\\end{align*}$$\n",
        "where:\n",
        "\n",
        "$$\\begin{align*}\n",
        "x_i&\\sim \\text{Normal}(\\text{loc}=\\boldsymbol{\\mu}_{z_i},\\,\\text{scale}=\\boldsymbol{\\sigma}_{z_i}) \\\\\n",
        "z_i &= \\text{Categorical}(\\text{prob}=\\boldsymbol{\\pi}),\\\\\n",
        "&\\,\\quad \\text{with}\\;\\boldsymbol{\\pi}=\\{\\pi_1,\\cdots,\\pi_K\\}\\\\\n",
        "\\boldsymbol{\\pi}&\\sim\\text{Dirichlet}(\\text{concentration}=\\{\\frac{\\alpha}{K},\\cdots,\\frac{\\alpha}{K}\\})\\\\\n",
        "\\alpha&\\sim \\text{InverseGamma}(\\text{concentration}=1,\\,\\text{rate}=1)\\\\\n",
        "\\boldsymbol{\\mu_j} &\\sim \\text{Normal}(\\text{loc}=\\boldsymbol{0}, \\,\\text{scale}=\\boldsymbol{1})\\\\\n",
        "\\boldsymbol{\\sigma_j} &\\sim \\text{InverseGamma}(\\text{concentration}=\\boldsymbol{1},\\,\\text{rate}=\\boldsymbol{1})\\\\\n",
        "\\end{align*}$$\n",
        "\n",
        "Our goal is to assign each $x_i$ to the $j$th cluster through $z_i$ which represents the inferred index of a cluster.\n",
        "\n",
        "For an ideal Dirichlet Mixture Model, $K$ is set to $\\infty$. However, it is known that one can approximate a Dirichlet Mixture Model with a sufficiently large $K$. Note that although we arbitrarily set an initial value of $K$, an optimal number of clusters is also inferred through optimization,  unlike a simple Gaussian Mixture Model.\n",
        "\n",
        "In this notebook, we use a bivariate Gaussian distribution as a mixture component and set $K$ to 30."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "oI9diwFoxfu6"
      },
      "outputs": [],
      "source": [
        "reset_sess()\n",
        "\n",
        "# Upperbound on K\n",
        "max_cluster_num = 30\n",
        "\n",
        "# Define trainable variables.\n",
        "mix_probs = tf.nn.softmax(\n",
        "    tf.Variable(\n",
        "        name='mix_probs',\n",
        "        initial_value=np.ones([max_cluster_num], dtype) / max_cluster_num))\n",
        "\n",
        "loc = tf.Variable(\n",
        "    name='loc',\n",
        "    initial_value=np.random.uniform(\n",
        "        low=-9, #set around minimum value of sample value\n",
        "        high=9, #set around maximum value of sample value\n",
        "        size=[max_cluster_num, dims]))\n",
        "\n",
        "precision = tf.nn.softplus(tf.Variable(\n",
        "    name='precision',\n",
        "    initial_value=\n",
        "    np.ones([max_cluster_num, dims], dtype=dtype)))\n",
        "\n",
        "alpha = tf.nn.softplus(tf.Variable(\n",
        "    name='alpha',\n",
        "    initial_value=\n",
        "    np.ones([1], dtype=dtype)))\n",
        "\n",
        "training_vals = [mix_probs, alpha, loc, precision]\n",
        "\n",
        "\n",
        "# Prior distributions of the training variables\n",
        "\n",
        "#Use symmetric Dirichlet prior as finite approximation of Dirichlet process.\n",
        "rv_symmetric_dirichlet_process = tfd.Dirichlet(\n",
        "    concentration=np.ones(max_cluster_num, dtype) * alpha / max_cluster_num,\n",
        "    name='rv_sdp')\n",
        "\n",
        "rv_loc = tfd.Independent(\n",
        "    tfd.Normal(\n",
        "        loc=tf.zeros([max_cluster_num, dims], dtype=dtype),\n",
        "        scale=tf.ones([max_cluster_num, dims], dtype=dtype)),\n",
        "    reinterpreted_batch_ndims=1,\n",
        "    name='rv_loc')\n",
        "\n",
        "\n",
        "rv_precision = tfd.Independent(\n",
        "    tfd.InverseGamma(\n",
        "        concentration=np.ones([max_cluster_num, dims], dtype),\n",
        "        rate=np.ones([max_cluster_num, dims], dtype)),\n",
        "    reinterpreted_batch_ndims=1,\n",
        "    name='rv_precision')\n",
        "\n",
        "rv_alpha = tfd.InverseGamma(\n",
        "    concentration=np.ones([1], dtype=dtype),\n",
        "    rate=np.ones([1]),\n",
        "    name='rv_alpha')\n",
        "\n",
        "# Define mixture model\n",
        "rv_observations = tfd.MixtureSameFamily(\n",
        "    mixture_distribution=tfd.Categorical(probs=mix_probs),\n",
        "    components_distribution=tfd.MultivariateNormalDiag(\n",
        "        loc=loc,\n",
        "        scale_diag=precision))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0vRyCpEsunyY"
      },
      "source": [
        "## 3. Optimization\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7vD2QQlyu9de"
      },
      "source": [
        "We optimize the model with Preconditioned Stochastic Gradient Langevin Dynamics (pSGLD), which enables us to optimize a model over a large number of samples in a mini-batch gradient descent manner. \n",
        "\n",
        "To update parameters $\\boldsymbol{\\theta}\\equiv\\{\\boldsymbol{\\pi},\\,\\alpha,\\, \\boldsymbol{\\mu_j},\\,\\boldsymbol{\\sigma_j}\\}$ in $t\\,$th iteration with mini-batch size $M$, the update is sampled as:\n",
        "\n",
        "$$\\begin{align*}\n",
        "\\Delta \\boldsymbol { \\theta } _ { t } & \\sim \\frac { \\epsilon _ { t } } { 2 } \\bigl[ G \\left( \\boldsymbol { \\theta } _ { t } \\right) \\bigl( \\nabla _ { \\boldsymbol { \\theta } } \\log p \\left( \\boldsymbol { \\theta } _ { t } \\right) \n",
        " + \\frac { N } { M } \\sum _ { k = 1 } ^ { M } \\nabla _ \\boldsymbol { \\theta } \\log \\text{GMM}(x_{t_k})\\bigr) + \\sum_\\boldsymbol{\\theta}\\nabla_\\theta G \\left( \\boldsymbol { \\theta } _ { t } \\right) \\bigr]\\\\\n",
        "&+ G ^ { \\frac { 1 } { 2 } } \\left( \\boldsymbol { \\theta } _ { t } \\right) \\text { Normal } \\left( \\text{loc}=\\boldsymbol{0} ,\\, \\text{scale}=\\epsilon _ { t }\\boldsymbol{1} \\right)\\\\\n",
        "\\end{align*}$$\n",
        "\n",
        "In the above equation, $\\epsilon _ { t }$ is learning rate at $t\\,$th iteration and $\\log p(\\theta_t)$ is a sum of log prior distributions of $\\theta$. $G ( \\boldsymbol { \\theta } _ { t })$ is a preconditioner which adjusts the scale of the gradient of each parameter. \n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "lWGANU8Gk_DN"
      },
      "outputs": [],
      "source": [
        "# Learning rates and decay\n",
        "starter_learning_rate = 1e-6\n",
        "end_learning_rate = 1e-10\n",
        "decay_steps = 1e4\n",
        "\n",
        "# Number of training steps\n",
        "training_steps = 10000\n",
        "\n",
        "# Mini-batch size\n",
        "batch_size = 20\n",
        "\n",
        "# Sample size for parameter posteriors\n",
        "sample_size = 100"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VHpt9UKmpdBI"
      },
      "source": [
        "We will use the joint log probability of the likelihood $\\text{GMM}(x_{t_k})$ and the prior probabilities $p(\\theta_t)$ as the loss function for pSGLD.\n",
        "\n",
        "Note that as specified in the [API of pSGLD](https://www.tensorflow.org/probability/api_docs/python/tfp/optimizer/StochasticGradientLangevinDynamics), we need to divide the sum of the prior probabilities by sample size $N$. "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "WRwRuk5Do2Cl"
      },
      "outputs": [],
      "source": [
        "# Placeholder for mini-batch\n",
        "observations_tensor = tf.compat.v1.placeholder(dtype, shape=[batch_size, dims])\n",
        "\n",
        "# Define joint log probabilities\n",
        "# Notice that each prior probability should be divided by num_samples and\n",
        "# likelihood is divided by batch_size for pSGLD optimization.\n",
        "log_prob_parts = [\n",
        "    rv_loc.log_prob(loc) / num_samples,\n",
        "    rv_precision.log_prob(precision) / num_samples,\n",
        "    rv_alpha.log_prob(alpha) / num_samples,\n",
        "    rv_symmetric_dirichlet_process.log_prob(mix_probs)[..., tf.newaxis]\n",
        "    / num_samples,\n",
        "    rv_observations.log_prob(observations_tensor) / batch_size\n",
        "]\n",
        "joint_log_prob = tf.reduce_sum(tf.concat(log_prob_parts, axis=-1), axis=-1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "PFlcZuS1ku4E"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Elapsed time: 309.8013095855713 seconds\n"
          ]
        }
      ],
      "source": [
        "# Make mini-batch generator\n",
        "dx = tf.compat.v1.data.Dataset.from_tensor_slices(observations)\\\n",
        "  .shuffle(500).repeat().batch(batch_size)\n",
        "iterator = tf.compat.v1.data.make_one_shot_iterator(dx)\n",
        "next_batch = iterator.get_next()\n",
        "\n",
        "# Define learning rate scheduling\n",
        "global_step = tf.Variable(0, trainable=False)\n",
        "learning_rate = tf.train.polynomial_decay(\n",
        "    starter_learning_rate,\n",
        "    global_step, decay_steps,\n",
        "    end_learning_rate, power=1.)\n",
        "\n",
        "# Set up the optimizer. Don't forget to set data_size=num_samples.\n",
        "optimizer_kernel = tfp.optimizer.StochasticGradientLangevinDynamics(\n",
        "    learning_rate=learning_rate,\n",
        "    preconditioner_decay_rate=0.99,\n",
        "    burnin=1500,\n",
        "    data_size=num_samples)\n",
        "\n",
        "train_op = optimizer_kernel.minimize(-joint_log_prob)\n",
        "\n",
        "# Arrays to store samples\n",
        "mean_mix_probs_mtx = np.zeros([training_steps, max_cluster_num])\n",
        "mean_alpha_mtx = np.zeros([training_steps, 1])\n",
        "mean_loc_mtx = np.zeros([training_steps, max_cluster_num, dims])\n",
        "mean_precision_mtx = np.zeros([training_steps, max_cluster_num, dims])\n",
        "\n",
        "init = tf.global_variables_initializer()\n",
        "sess.run(init)\n",
        "\n",
        "start = time.time()\n",
        "for it in range(training_steps):\n",
        "  [\n",
        "      mean_mix_probs_mtx[it, :],\n",
        "      mean_alpha_mtx[it, 0],\n",
        "      mean_loc_mtx[it, :, :],\n",
        "      mean_precision_mtx[it, :, :],\n",
        "      _\n",
        "  ] = sess.run([\n",
        "      *training_vals,\n",
        "      train_op\n",
        "  ], feed_dict={\n",
        "      observations_tensor: sess.run(next_batch)})\n",
        "\n",
        "elapsed_time_psgld = time.time() - start\n",
        "print(\"Elapsed time: {} seconds\".format(elapsed_time_psgld))\n",
        "\n",
        "# Take mean over the last sample_size iterations\n",
        "mean_mix_probs_ = mean_mix_probs_mtx[-sample_size:, :].mean(axis=0)\n",
        "mean_alpha_ = mean_alpha_mtx[-sample_size:, :].mean(axis=0)\n",
        "mean_loc_ = mean_loc_mtx[-sample_size:, :].mean(axis=0)\n",
        "mean_precision_ = mean_precision_mtx[-sample_size:, :].mean(axis=0)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zjosnQ4yp3Za"
      },
      "source": [
        "## 4. Visualize the result"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IHzhAFUmz7re"
      },
      "source": [
        "### 4.1. Clustered result"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gey5YIL0p641"
      },
      "source": [
        "First, we visualize the result of clustering.\n",
        "\n",
        "\n",
        "For assigning each sample $x_i$ to a cluster $j$, we calculate the posterior of $z_i$ as:\n",
        "\n",
        "$$\\begin{align*}\n",
        "j =  \\underset{z_i}{\\arg\\max}\\,p(z_i\\,|\\,x_i,\\,\\boldsymbol{\\theta})\n",
        "\\end{align*}$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "BSDDRGFikobg"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Number of inferred clusters = 3\n",
            "\n",
            "Number of elements in each cluster = [16911 16645 16444]\n",
            "\n"
          ]
        },
        {
          "data": {
            "image/png": 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8jsjyJ8l1H9vuYxFWmqLZN2OVDyN+yu4rBoSZJrLiKXwNH5Mcd+Pn/Akq+5sK7oqiHBL0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hqt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\nQRAEQehhRHAXBEEQhB7m/wOAxHz4XbiewAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 576x396 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "loc_for_posterior = tf.compat.v1.placeholder(\n",
        "    dtype, [None, max_cluster_num, dims], name='loc_for_posterior')\n",
        "precision_for_posterior = tf.compat.v1.placeholder(\n",
        "    dtype, [None, max_cluster_num, dims], name='precision_for_posterior')\n",
        "mix_probs_for_posterior = tf.compat.v1.placeholder(\n",
        "    dtype, [None, max_cluster_num], name='mix_probs_for_posterior')\n",
        "\n",
        "# Posterior of z (unnormalized)\n",
        "unnomarlized_posterior = tfd.MultivariateNormalDiag(\n",
        "    loc=loc_for_posterior, scale_diag=precision_for_posterior)\\\n",
        "   .log_prob(tf.expand_dims(tf.expand_dims(observations, axis=1), axis=1))\\\n",
        "   + tf.log(mix_probs_for_posterior[tf.newaxis, ...])\n",
        "\n",
        "# Posterior of z (normarizad over latent states)\n",
        "posterior = unnomarlized_posterior\\\n",
        "  - tf.reduce_logsumexp(unnomarlized_posterior, axis=-1)[..., tf.newaxis]\n",
        "\n",
        "cluster_asgmt = sess.run(tf.argmax(\n",
        "    tf.reduce_mean(posterior, axis=1), axis=1), feed_dict={\n",
        "        loc_for_posterior: mean_loc_mtx[-sample_size:, :],\n",
        "        precision_for_posterior: mean_precision_mtx[-sample_size:, :],\n",
        "        mix_probs_for_posterior: mean_mix_probs_mtx[-sample_size:, :]})\n",
        "\n",
        "idxs, count = np.unique(cluster_asgmt, return_counts=True)\n",
        "\n",
        "print('Number of inferred clusters = {}\\n'.format(len(count)))\n",
        "np.set_printoptions(formatter={'float': '{: 0.3f}'.format})\n",
        "\n",
        "print('Number of elements in each cluster = {}\\n'.format(count))\n",
        "\n",
        "def convert_int_elements_to_consecutive_numbers_in(array):\n",
        "  unique_int_elements = np.unique(array)\n",
        "  for consecutive_number, unique_int_element in enumerate(unique_int_elements):\n",
        "    array[array == unique_int_element] = consecutive_number\n",
        "  return array\n",
        "\n",
        "cmap = plt.get_cmap('tab10')\n",
        "plt.scatter(\n",
        "    observations[:, 0], observations[:, 1],\n",
        "    1,\n",
        "    c=cmap(convert_int_elements_to_consecutive_numbers_in(cluster_asgmt)))\n",
        "plt.axis([-10, 10, -10, 10])\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OrAmMfKiw5LD"
      },
      "source": [
        "We can see an almost equal number of samples are assigned to appropriate clusters and the model has successfully inferred the correct number of clusters as well.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4AX1UBDlNXNp"
      },
      "source": [
        "### 4.2. Visualize uncertainty"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pN_w3vrozBIB"
      },
      "source": [
        "Here, we look at the uncertainty of the clustering result by visualizing it for each sample.\n",
        "\n",
        "We calculate uncertainty by using entropy:\n",
        "\n",
        "$$\\begin{align*}\n",
        "\\text{Uncertainty}_\\text{entropy} =  -\\frac{1}{K}\\sum^{K}_{z_i=1}\\sum^{O}_{l=1}p(z_i\\,|\\,x_i,\\,\\boldsymbol{\\theta}_l)\\log p(z_i\\,|\\,x_i,\\,\\boldsymbol{\\theta}_l)\n",
        "\\end{align*}$$\n",
        "\n",
        "In pSGLD, we treat the value of a training parameter at each iteration as a sample from its posterior distribution. Thus, we calculate entropy over values from $O$ iterations for each parameter. The final entropy value is calculated by averaging entropies of all the cluster assignments."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "4WgWky_KzJ2W"
      },
      "outputs": [],
      "source": [
        "# Calculate entropy\n",
        "posterior_in_exponential = tf.exp(posterior)\n",
        "uncertainty_in_entropy = tf.reduce_mean(-tf.reduce_sum(\n",
        "    posterior_in_exponential\n",
        "    * posterior,\n",
        "    axis=1), axis=1)\n",
        "\n",
        "uncertainty_in_entropy_ = sess.run(uncertainty_in_entropy, feed_dict={\n",
        "    loc_for_posterior: mean_loc_mtx[-sample_size:, :],\n",
        "    precision_for_posterior: mean_precision_mtx[-sample_size:, :],\n",
        "    mix_probs_for_posterior: mean_mix_probs_mtx[-sample_size:, :]\n",
        "})"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "w35imrT45DG3"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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Ggo5CsVFqyfBtyrgbxcPCI8+OCGkKOpqE3IPoIhyGkeQEquRCVJ1iHz9gS3vx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\nbXe+MynYAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 576x396 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.title('Entropy')\n",
        "sc = plt.scatter(observations[:, 0],\n",
        "                 observations[:, 1],\n",
        "                 1,\n",
        "                 c=uncertainty_in_entropy_,\n",
        "                 cmap=plt.cm.viridis_r)\n",
        "cbar = plt.colorbar(sc,\n",
        "                    fraction=0.046,\n",
        "                    pad=0.04,\n",
        "                    ticks=[uncertainty_in_entropy_.min(),\n",
        "                           uncertainty_in_entropy_.max()])\n",
        "cbar.ax.set_yticklabels(['low', 'high'])\n",
        "cbar.set_label('Uncertainty', rotation=270)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CMNSqtee5nNd"
      },
      "source": [
        "In the above graph, less luminance represents more uncertainty. \n",
        "We can see the samples near the boundaries of the clusters have especially higher uncertainty. This is intuitively true, that those samples are difficult to cluster."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zKbNv-Pa0Emp"
      },
      "source": [
        "### 4.3. Mean and scale of selected mixture component"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JMFLSd4T04Fx"
      },
      "source": [
        "Next, we look at selected clusters' $\\mu_j$ and $\\sigma_j$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "g6KSqkChw1Mu"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Component id = 0, Number of elements = 16911\n",
            "Mean loc = [-4.030 -4.113], Mean scale = [ 0.994  0.972]\n",
            "\n",
            "Component id = 4, Number of elements = 16645\n",
            "Mean loc = [ 3.999  4.069], Mean scale = [ 1.038  1.046]\n",
            "\n",
            "Component id = 5, Number of elements = 16444\n",
            "Mean loc = [-0.005 -0.023], Mean scale = [ 0.967  1.025]\n",
            "\n"
          ]
        }
      ],
      "source": [
        "for idx, numbe_of_samples in zip(idxs, count):\n",
        "  print(\n",
        "      'Component id = {}, Number of elements = {}'\n",
        "      .format(idx, numbe_of_samples))\n",
        "  print(\n",
        "      'Mean loc = {}, Mean scale = {}\\n'\n",
        "      .format(mean_loc_[idx, :], mean_precision_[idx, :]))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ryK25yAz1ItV"
      },
      "source": [
        "Again, the $\\boldsymbol{\\mu_j}$ and $\\boldsymbol{\\sigma_j}$ close to the ground truth."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m6ut4VFo0-TB"
      },
      "source": [
        "### 4.4 Mixture weight of each mixture component"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "p-BPkMA-yaQe"
      },
      "source": [
        "We also look at inferred mixture weights."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "D5gJpzu9WJBi"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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cc0+nGjxzUZ4v9ikrK/P6b3eF7mrX1zp7XGbtD084HI4effznoj/c0R/u6A93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\nAJgM4Q4AgMkQ7gAAmMz/A75pXTYTVKVrAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 576x396 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.ylabel('Mean posterior of mixture weight')\n",
        "plt.xlabel('Component')\n",
        "plt.bar(range(0, max_cluster_num), mean_mix_probs_)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "siNFZC1R1Rux"
      },
      "source": [
        "We see only a few (three) mixture component have significant weights and the rest of the weights have values close to zero. This also shows the model successfully inferred the correct number of mixture components which constitutes the distribution of the samples."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H4N4nkY6B39E"
      },
      "source": [
        "### 4.5. Convergence of $\\alpha$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9AXYHzAbB-0X"
      },
      "source": [
        "We look at convergence of Dirichlet distribution's concentration parameter $\\alpha$."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "xG31_8KxB7zk"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Value of inferred alpha = 0.679\n",
            "\n"
          ]
        },
        {
          "data": {
            "image/png": 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sLc/V/P8JLq+yLbf2MYM0UUNiGaRD21Jaef/99+NeGYqjFI5dirGXQT79kO6Y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\nFGkhhBDCTUmRFkIIIdyUFGkhhBDCTf0HdVNNUcjt6G8AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 576x396 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "print('Value of inferred alpha = {0:.3f}\\n'.format(mean_alpha_[0]))\n",
        "plt.ylabel('Sample value of alpha')\n",
        "plt.xlabel('Iteration')\n",
        "plt.plot(mean_alpha_mtx)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vIO7TOO-CKPH"
      },
      "source": [
        "Considering the fact that smaller $\\alpha$ results in less expected number of clusters in a Dirichlet mixture model, the model seems to be learning the optimal number of clusters over iterations."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "G6Q4Wyaw30Er"
      },
      "source": [
        "### 4.6. Inferred number of clusters over iterations"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RYg3FeAt564F"
      },
      "source": [
        "We visualize how the inferred number of clusters changes over iterations.\n",
        "\n",
        "To do so, we infer the number of clusters over the iterations."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "wT4v6n8P5_C2"
      },
      "outputs": [],
      "source": [
        "step = sample_size\n",
        "num_of_iterations = 50\n",
        "estimated_num_of_clusters = []\n",
        "interval = (training_steps - step) // (num_of_iterations - 1)\n",
        "iterations = np.asarray(range(step, training_steps+1, interval))\n",
        "for iteration in iterations:\n",
        "  start_position = iteration-step\n",
        "  end_position = iteration\n",
        "\n",
        "  result = sess.run(tf.argmax(\n",
        "      tf.reduce_mean(posterior, axis=1), axis=1), feed_dict={\n",
        "          loc_for_posterior:\n",
        "              mean_loc_mtx[start_position:end_position, :],\n",
        "          precision_for_posterior:\n",
        "              mean_precision_mtx[start_position:end_position, :],\n",
        "          mix_probs_for_posterior:\n",
        "              mean_mix_probs_mtx[start_position:end_position, :]})\n",
        "\n",
        "  idxs, count = np.unique(result, return_counts=True)\n",
        "  estimated_num_of_clusters.append(len(count))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "uG2m9gEi4Bmi"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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Y++6775LG8WvtO8OGbzA3rcNQ8RYRCXiVFu+NGzdyxRVX8PXXX1d68rXXXutw\ngHONSRYtWlR2rF+/foSGhgKlHcr++9//ViXmgGO07Yhps5Wue9/Ww+pwRETEYpUW79WrV3PFFVfw\n5ZdfVnqyM8U7KCiIoKCgcsfCw8MBsNvtLFmyhLvvvtvZeAOSERUDKa1h11bMnJMYcQmOTxIREb/l\nsKuYu/y2MYndbmf69OnUrVuXHj10N+lI3odzyZ49lYQhTxHd9Q6rwxEREQtZtuvHzJkzqVOnjtOF\nO9C6iv2W2bgVACe/+oLctp0ti8PX8+gtlEf3UB7dQ3l0D6/oKladVq1aRXBwMD179rRieJ9k1K4L\ndRrA9gzMoiKrwxEREQtVeud96tQpoqOjy/7tqooak+Tk5BAaGlq253n9+vXp16+fy2MECiO1M+bn\n78OOTZBq3d23iIhYq9LiPXr0aKZNm8aYMWOYMmWKywNU1phEqu5c8TY3rcdQ8RYRCViVFu/Q0FAG\nDhxITk4OQ4cOrfAz06ZNq7bApAJNW0BMHOam9Zh2O4a2rBURCUiVFu+0tDT279/P9OnTGTBggCdj\nkkoYtiCMdh0xv/kS9u2Cpi2tDklERCxQafGOjIzksssuY8KECSQlJXHs2DFyc3OJi4ujZs2anoxR\nzmOkXoX5zZelU+cq3iIiAcnhq2K5ubk8/fTTnDp1isjISE6dOkWNGjX461//Sv369T0Ro5yvdXsI\nDindbe1/77c6GhERsYDD4v3Pf/6TPn36cNVVV5Ud+/rrr3nttddIS0ur1uDkQkZYOFyWCpu/w8w8\nilEz2eqQRETEwxw+8VRQUFCucEPptqi5ublOD3LgwAEGDx7M559/Xnbs008/5Z577qGwsLAK4QqA\n0b70SXP1+BYRCUwOi3doaCg//vhjuWO7du0iLCzMqQEq6ir21VdfkZOTQ0KC9uh2hdGuE6DiLSIS\nqBxOmz/wwANMnDiRGjVqEB0dTW5uLjk5OQwbNsypASrqKta5c2ciIiIu2rFMKmfE14DGzeHHLZj5\npzCiXN9ER0REfI/D4t2mTRtmzJjB7t27y542T0lJcfrOu6KuYhEREVUO9GJ7vHryGt4i59qbyJ27\ni4RjB4n83U0eHduf8mgl5dE9lEf3UB7dw1N5dKoxSXh4eLlpbysEemOS3zJr1QMg6/v1ZDe5zGPj\n+lseraI8uofy6B7Ko3v4fWMScYNGzQAw9+22OBAREfE0FW8fZURGQ626sH83HmrJLiIiXsLhtPmn\nn37Kbbfd5vIAFXUVa9euHT/88APZ2dk899xztGjRgvvuu8/lMQKV0TgFc/1KyDwKtepYHY6IiHiI\nw+L9zTffcP3117vcFrSyrmIVEC3xAAAdG0lEQVR33nmnS9eT8zRKgfUrMffvxlDxFhEJGA6Ld8OG\nDXn88cdJSUm5oICrYYm1jMYpmAD7dkOn6yyORkREPMVh8U5MTOTGG2/0RCxSVQ2bgmFg7tdDayIi\ngcRh8e7RowcApmmSl5dHbGxstQclzjHCIyG5fulDa+rvLSISMBz+bX/q1CkmT57Mvffey9/+9jcA\n5syZc8GWqWINo1EKFJ6GY3pHU0QkUDgs3tOmTaNp06a8+uqrZWve1157Lf/617+cHuS3jUmOHz/O\n+PHjGTt2LJMnT+bMmTMuhi80TgH0vreISCBxWLyPHj3KHXfcUe5htZSUFE6fPu3UABU1JlmwYAFd\nu3ZlwoQJJCcns3z5chdCF/jlzhtA694iIgHDYfEOCwvj0KFD5Y4dO3bsgv3KK3OuMcn5HcS2bt1K\nx44dAejYsSM//PBDVWKW8zVoCoZNd94iIgHE4QNrvXr1YvTo0bRp04bs7GwmT57Mjh07nH5NrKLG\nJEVFRYSEhAAQGxtLdna2C6ELgBEWBnUbwIE9mPazGDbn/qNKRER8l8Pi3alTJyZNmkRGRgbNmzcn\nISGBvn37Eh8f74n4yqirWOWyWrcj/z/7qXW2mJD6zap9PH/No6cpj+6hPLqH8ugeXtVVrLCwEJvN\nhmEYlJSUUFBQcEnFOzw8nOLiYkJDQ8nKyio3pV4ZdRWrnL1maYexn79djS2k6u1Wq8Kf8+hJyqN7\nKI/uoTy6h1d1FXvnnXcYP348GRkZHDlyhI0bNzJmzBg++OADlwNq27Yta9euBWDt2rW0b9/e5WtJ\n6U5rQOlOayIi4vcc3nmvXLmSqVOnltucJScnh1GjRjm1P3lFjUmGDBlCeno6S5cuJSkpid///veX\n9lMEuvqNIShIO62JiAQIh8U7Jibmgl3VYmNjnd5prbLGJGPGjHEuQnHICAmFeo3g4H8xS0owgp1a\nDRERER9V6d/yO3fuBH59YO26664jNjaWU6dO8c0333D11Vd7LEhxzGiUgnlgL/x0EBo0sTocERGp\nRpUW75deeqnc1/v27Sv39Z49e/jTn/5ULUGJCxqnwKovMPftwlDxFhHxa5UW7/T0dE/GIZfIaNS8\ntD3o/t1w3a1WhyMiItXI4eJoZmYmy5cvJysrC7vdXu57AwcOrLbApIrqNYTgYO20JiISABwW7xde\neIF69erRsGFDbGo56bWM4BCo36T0obUzZzB+2cFORET8j8PibbfbGT58uFsHtdvtvPbaaxw8eJDg\n4GD69+9PvXr13DpGIDIap2Du2wVH9sO5hiUiIuJ3HN5KX3fddaxcuZLi4mK3Dfrdd99RUFDAM888\nwyOPPMJbb73ltmsHtEZqDyoiEggc3nlHRUXx2muvVfgA27vvvuvSoD/99BMpKaWFJjk5mczMTOx2\nu6blL5HROOXXh9ZERMRvOSze7733HsOGDXPrmnfDhg355JNP6N69O0ePHuXYsWPk5uZ6vNmJ36nT\nEEJDS6fORUTEbzks3rVr16Z9+/ZuvSvu0KEDO3fuZNy4cTRs2NCp9W51FXPOz81aUfzjVpJrJGIL\nC6+WMQIhj56gPLqH8ugeyqN7eE1XsY4dOzJx4kSuvPJKIiLKd6y69tprXR64d+/eZX8ePHiww+1W\n1VXMOfa6jWD7D/z07RqMpi3dfv1AyWN1Ux7dQ3l0D+XRPTzZVcxh8d60aRMAq1evvuB7rhbvffv2\n8emnnzJw4EAyMjJo0qSJ1rvd5dxDa/t3V0vxFhER6zks3uPGjXP7oA0bNsQ0TZ588klCQ0MZPHiw\n28cIVGUPremJcxERv+WweL/yyiuVfm/AgAEuDWqz2Rg0aJBL54oDtetCWITag4qI+DGHc9WJiYnl\n/gkLC2Pbtm3ExcV5Ij6pIsMWBI2awpGDmEWFVocjIiLVwOGdd48ePS44duedd6pxiRczGqVg/rgV\nDu6FlNZWhyMiIm7m0lNiMTExejLRm2mnNRERv+bwznvWrFkYhlH2td1u5+DBgyQlJVVrYOI6o3Fz\n7bQmIuLHHBbvGjVqlPvaZrPRsmVLunTpUm1BySWqmQwRUbrzFhHxUy6teV+qwsJCZsyYQX5+PmfO\nnOHuu++mffv2bh8nUBk2GzRqBjs3Y54uwIiItDokERFxo0qLd1pa2kVPNAyDsWPHujToihUrqFu3\nLn369CErK4sJEyYwdepUl64lFTMapWDu+AEO7IWWl1sdjoiIuFGlxbuyO+6TJ0+ycOFCSkpKXB40\nJiaG/fv3A5Cfn09MTIzL15KKndusxdy/C0PFW0TErximaZrOfLCkpIR///vffP7553Tr1o3bb7+d\nkJAQlwd+9tlnOXr0KPn5+YwcOZIWLVq4fC25UMmxo/z00O2Ed7qWmuM1qyEi4k8crnkDrFu3jrlz\n59K6dWtefPHFS27duXLlSpKSkhg9ejT79u1j1qxZvPDCCxc9R41JXFCvEYUZ6zn8370YbuowFpB5\nrAbKo3soj+6hPLqH1zQm2bdvH3PmzAFg+PDhNGnSxC0B7dy5k9TUVAAaN27MyZMnsdvtak7iZkZq\nZ8xPF8L2DGivtwNERPxFpcV71qxZbN++nXvuucftr4UlJyeze/duunTpQmZmJuHh4Src1eBc8TYz\n1mOoeIuI+I1Ki/fy5csBmDJlSqUnv/vuuy4NessttzBz5kzGjRuH3W6nf//+Ll1HHGjcHGLjMX/4\nFtN+tnTfcxER8XmVFm9XC7MzwsPDGT58eLVdX0oZNlvp3feqL+C/u6BZK6tDEhERN9BctZ8zUjsD\nYG5aZ3EkIiLiLire/q5VKoSGYmastzoSERFxExVvP2eEhcFl7eGng5jH9CqIiIg/UPEOAL9OnX9r\ncSQiIuIOTm3S4m7Lli1j5cqVZV/v2bOHt956y4pQAoKR2gnTMDA3rYdb/mx1OCIicoksKd433ngj\nN954IwDbtm1j9erVVoQRMIzYBGjSAnZtxczPw4jSXvIiIr7M8mnz9957j7vvvtvqMPyekdoZ7HbM\nzRusDkVERC6RpcV79+7d1KhR45L3ShfHjNSrSv+wSU+di4j4Oqe7ilWHV199ld/97ne0adPGqhAC\nhmma/NTvDuw52dR7eynGJXSEExERa1my5n3O1q1b6du3r1OfVVexS2e//ErMpYs58tUXGK07uHQN\n5dE9lEf3UB7dQ3l0D092FbNs2jwrK4vw8HCCgy3974eAUvbKmDZsERHxaZYV7+zsbOLi4qwaPjCl\ntIbIKMxN67FwtURERC6RZcW7adOmjBo1yqrhA5IRHIxxeUfIyoRD+6wOR0REXGT5q2LiYe3VqERE\nxNepeAcYo80VEBSkdW8RER+m4h1gjMgoaHE57N+NefKE1eGIiIgLVLwD0LkNW8wf1KhERMQXqXgH\nICO1E0BpoxIREfE5lr1kvWrVKhYvXozNZqNXr15cccUVVoUScIyk2lC/MWzfhFl4GiM8wuqQRESk\nCiy5887Ly+O9995jwoQJjBw5km+/1fStpxmpnaHkDGzLsDoUERGpIkuK9+bNm2nbti0REREkJCQw\nYMAAK8IIaGXr3po6FxHxOZY0Jlm0aBGHDx/m1KlT5Ofn06NHD9q2bevpMAKaabdz5MHboKSEunOX\nYAQFWR2SiIg4ybI177y8PB5//HEyMzNJS0tj5syZGIZR6efVmMT9zMuvxFy5hCPfLMdIae3UOcqj\neyiP7qE8uofy6B5+35gkLi6Oli1bEhQURHJyMhEREeTm5loRSkBToxIREd9kSfFOTU1ly5Yt2O12\n8vLyKCwsJCYmxopQAlurdhAapnVvEREfY8m0eWJiIl26dGH06NEA9O3bF5tNr5x7mhEaBq07QMZa\nzKOHMZLrWR2SiIg4wbI171tuuYVbbrnFquHlF0b7zpgZazF/WI+R/L9WhyMiIk7Q7W6AM9p2BMPQ\n1LmIiA9R8Q5wRmw8NG0Ju7ZjntJDgyIivkDFW0o3bDHtmJs3WB2KiIg4QcVbMNr/8srYpnUWRyIi\nIs6w5IG1rVu3MnnyZBo0aABAw4YN6du3rxWhCEByfahVB7Z8j3nmDEZIiNURiYjIRVj2tHnr1q35\n29/+ZtXwch7DMDBSO2P+5yPYuRkuV4c3ERFvpmlzAdSoRETEl1hWvA8dOsSLL77ImDFj+OGHH6wK\nQ85JuQwiozE3rcfZXjXm0UOcnTgSc/f2ag5ORETOZ0lXsaysLHbs2MHVV1/Nzz//TFpaGtOnTyc4\n2LJZfAFO/H0MBcs/o/ZLcwlt1uqinzVNk8yRAyjaspHgeg1JTn8HIyTUQ5GKiAQ2y7ZHveaaawBI\nTk4mPj6erKwsatWqVek56ipW/cwWbWH5Zxz7zyfYImIr/My5PNrXLMfcshHCIig5fIDDc2Zi697T\nwxH7Lv0+uofy6B7Ko3v4fVexVatWsXjxYgCys7PJyckhMTHRilDkfG2ugKBgh+veZv4pzIWvQ2go\ntpEvQlwC5icLMDOPeihQEZHAZknx7tixI9u2bWPs2LFMnDiRfv36acrcCxgRkdCyLRzYg5l1vNLP\nmYvmQl4Oxu29Meo3xujRF84UY3/7VafXy0VExHWWVMyIiAhGjhxpxdDigNG+M+a270sblfzhtgu+\nX7xrG+ZXn0FyfYxb/lx6TufrMb/+D2z+Djatg/ZdPB22iEhA0atiUo7R7txuaxdOnZv2s2SlvwCm\nie3eRzCCSzdzMQwDW59HICgY+9uvYRYVejRmEZFAo+It5Rg1akKDJrDjB8zCgnLfM1cu4cyubRhX\n/R6jVbvy59Wpj9H1fyErE/OTdz0ZsohIwFHxlgsYqVdBSQlszSg7ZuaexPzgLYzIqNI17orOu60n\n1KiF+cUizCMHPBWuiEjAUfGWC1TUqMR8bw6czifugYEYcQkVnxcWhu2ev8DZs9jnv6KH10REqomK\nt1yoYTOIT8Tc/B3m2bOYO7dgrlkODZsSfdvdFz3VSO0MqZ1h52bMdV95KGARkcBiafEuLi5m8ODB\nrFixwsow5DfONSrhVB78uAX7vJfBMLDd+yhGUJDD8229+0NoKObC1zELTnkgYhGRwGJp8X7//feJ\njo62MgSpxLlGJfY3psFPBzGu64rRtKVz5ybVxujeC3KzMRfNq84wRUQCkmU7oxw+fJhDhw7RoUMH\nq0KQi2nVFsLC4eRxiI7FuPP+Kp1u3HoH5prlmCs+w96sVaXr5ADUqIVRM/kSAxYRCRyWFe8333yT\nhx9+WFPmXsoICS3dLnXjaoy7H8KIiqna+cEh2PoMwD55DObsf3DRR9fCwrGlzcCoUfne9iIi8itL\nuop99dVXHD9+nLvuuosFCxZQq1Yt/vCHP3g6DHGg5NhPFG3NIPIP3TAMw6VrFHy1hDOH91f6/bPH\nj5G/ZBERV/+BpKf+7mqoIiIBxZI7740bN3Ls2DE2btzIiRMnCAkJITExkXbt2lV6jrqKWaRlKjk/\n/VT2ZZXz2Lxt6T+VME0T9v7I6TUrOPzZRxipnS4lWp+h30f3UB7dQ3l0D092FbOkeA8bNqzsz+fu\nvC9WuMV/Gb88xW5/+q/Y334FW6t2GGFhVoclIuLV9J63WM6o1wjj5j/BiWOYny20OhwREa9nefHu\n2bOn1rsF4/bekJCEueQDzKOHrA5HRMSrWV68RQCM8AhsvftBSYm2VhURcUDFW7xHh6vh8ith+ybM\n7762OhoREa+l4i1eo7Qv+AAICcV895+YpwscnyQiEoBUvMWrGDWTMW67G3KyMBfPtzocERGvpOIt\nXsfoeifUqov55ceYB/ZaHY6IiNexpHgXFRUxefJkxo0bx6hRo9iwYYMVYYiXMkJCS6fPTTv2+bMw\n7XarQxIR8SqWbNKyYcMGmjVrxp///GcyMzN55plnuPLKK60IRbyU0aYDRsdrMb/7GvObpRjX3Wp1\nSCIiXsOS4n3NNdeU/fnEiRMkJiZaEYZ4OaPnw5ibN2C+9wb2rd9bHY5bHY+IwH76tNVh+Dzl0T2U\nRzcIDaPkL8M9NpwljUnOeeqppzhx4gQjR46kUaNGVoUhXizv4wVkvzzR6jBERC7OMEgaP42Ijtc4\n/qw7hrOyeAPs27ePGTNmMGnSpIt2rlJjEu9gRR7N/FNwtsSjY1a35ORkjh49anUYPk95dA/l0Q2C\nQ6iX0ty/G5Ps3buX2NhYkpKSaNy4MWfPniU3N5e4uDgrwhEvZ0RFWx2C2wXFJ2IUFFodhs9THt1D\nefQ9ljxtvm3bNj7++GMAsrOzKSwsJCYmxopQREREfI4ld9633norL7/8MmPHjqW4uJiHH34Ym02v\nnIuIiDjDkuIdGhrK0KFDrRhaRETE5+l2V0RExMeoeIuIiPgYFW8REREfo+ItIiLiYyx5YA1g7ty5\nbN++Hbvdzh133MFVV11lVSgiIiI+xZLivWXLFg4ePMizzz5LXl4eTzzxhIq3iIiIkywp3q1btyYl\nJQWAqKgoioqKsNvtetdbRETECZZUS5vNRnh4OADLli2jQ4cOKtwiIiJOsrQxybfffsuHH37IU089\nRWRkpFVhiIiI+BTLbnczMjL44IMPGDVqlAq3iIhIFVhSvAsKCpg7dy4jR44kOtr/OkaJiIhUJ0um\nzZcuXcrChQupU6dO2bHHHnuMpKQkT4ciIiLicyxd8xYREZGq0yPeIiIiPkbFW0RExMdYtj2qp8yZ\nM4ddu3ZhGAb/93//V7Y5jJT32+1qmzVrxowZM7Db7cTHxzN48GBCQkJYtWoVn376KYZhcPPNN3Pj\njTdSUlLCzJkzyczMxGazMXDgQGrXrm31j2SZ4uJi/va3v3HXXXdx+eWXK48uWLVqFYsXL8Zms9Gr\nVy8aNmyoPFZRYWEhM2bMID8/nzNnznD33XcTHx/P7NmzMQyDhg0b0r9/fwAWL17MmjVrMAyDu+++\nmyuuuIKCggKmTZtGQUEB4eHhDB06NKAeMD5w4ACTJk2ie/fudOvWjePHj1/y7+C+ffsqzL9LTD+2\ndetW8/nnnzdN0zQPHjxojho1yuKIvNPmzZvN5557zjRN08zNzTUfeeQRMz093Vy9erVpmqY5b948\nc8mSJebp06fNIUOGmPn5+WZRUZE5fPhwMy8vz1y+fLn52muvmaZpmhkZGebkyZMt+1m8wfz5882R\nI0eay5cvVx5dkJubaw4ZMsQsKCgws7KyzFmzZimPLvjss8/MefPmmaZpmidOnDCHDh1qjh8/3ty1\na5dpmqY5depUc+PGjebPP/9sPvHEE+aZM2fMnJwcc+jQoebZs2fNBQsWmB999JFpmqb5n//8x3zr\nrbcs+1k87fTp0+b48ePNWbNmmZ999plpmqZbfgcryr+r/HrafPPmzXTq1AmA+vXrk5+fT0FBgcVR\neZ/WrVszbNgw4Nftardu3UrHjh0B6NixIz/88AO7d++mWbNmREZGEhoaSsuWLdmxYwdbtmyhc+fO\nALRt25adO3da9rNY7fDhwxw6dIgOHToAKI8u2Lx5M23btiUiIoKEhAQGDBigPLogJiaGvLw8APLz\n84mOjubYsWNls49XXnklmzdvZsuWLXTo0IHg4GBiY2OpWbMmhw4dKpfHc58NFCEhITz55JMkJCSU\nHbvU38GSkpIK8+8qvy7e2dnZxMbGln0dGxtLdna2hRF5p4q2qy0qKiIkJAT4NW+V5fP84zabDcMw\nKCkp8fwP4gXefPNNHnzwwbKvlceqO3bsGEVFRbz44ouMHTuWzZs3K48u+N3vfsfx48cZPHgw48aN\n4/777ycqKqrs+3FxcZw8ebLCPP72eFxcXED93RkUFERoaGi5Y5f6O5idnV1h/l3l18X7t0y9FXdR\n3377LcuWLePhhx++pOsEap6/+uorWrRoQa1atdxyvUDNI0BeXh4jRoxg4MCBzJw585JyEah5XLly\nJUlJSUyfPp2xY8cyffr0ct+vLC8VHQ/UHLpLdeTUrx9YS0hIKPdfiydPniw3DSK/Ordd7ejRo4mM\njCQ8PJzi4mJCQ0PJysoiISHhgnxmZWXRvHnzcsdLSkowTZPgYL/+1arQxo0bOXbsGBs3buTEiROE\nhIQojy6Ii4ujZcuWBAUFkZycTEREBEFBQcpjFe3cuZPU1FQAGjduTHFxMWfPni37/rk8JiYmcuTI\nkbLj5/6ePJfHyMjIss8Gskv9/3J8fHzZMsa5z15KTv36zjs1NZW1a9cCsHfvXhISEoiIiLA4Ku9T\n0Xa1bdu2Lcvd2rVrad++Pc2bN2fPnj3k5+dTWFjIzp07ueyyy8rlecOGDbRp08ayn8VKw4YN4/nn\nn+fZZ5/lxhtv5K677lIeXZCamsqWLVuw2+3k5eVRWFioPLogOTmZ3bt3A5CZmUlERAT16tVjx44d\nAKxfv5727dtz+eWXs3HjRkpKSsjKyiIrK4v69evTrl071qxZA8C6deto3769ZT+LN7jU38Hg4OAK\n8+8qv99hbd68eWzfvh3DMHj44Ydp3Lix1SF5nYq2qx00aBCzZs3izJkzJCUlMXDgQIKDg1m7di2L\nFy/GMAy6devGddddh91uZ9asWfz000+EhIQwcODAgN/qdsGCBdSqVYvU1FRmzJihPFbRf/7zH5Yt\nWwbAXXfdVfbqovLovMLCQmbOnElOTg52u51evXoRHx/Pq6++immapKSklD2f8dlnn/H1118D0Lt3\nb9q2bUthYSEvvfQSp06dIjIykiFDhgRME6m9e/fy5ptvkpmZSVBQEImJiQwZMoT09PRL+h08dOhQ\nhfl3hd8XbxEREX/j19PmIiIi/kjFW0RExMeoeIuIiPgYFW8REREfo+ItIiLiY1S8RfzIoEGD2LFj\nB7t27WL//v1uvXZGRgbHjx8HYP78+XzxxRduvb6IOE/FW8QPLV++3O3F+5NPPikr3n369OHWW291\n6/VFxHmBt2egiJ/bunUrK1euZMOGDeTm5tK9e3fef/99Vq1axZkzZ+jUqRMPPvggNpuN8ePH07Jl\nS9avX88jjzxC7dq1SU9PJzMzkzNnzvA///M/3H777bzzzjts2bKFw4cPc9999/H999+TnJzMXXfd\nxf79+5k9ezZ5eXmEhIRw77330r59e7Zu3cr8+fNp06YN3377LcXFxQwaNIjWrVtbnSIRn6c7bxE/\n06ZNG1JSUrj33nu5/fbbWbVqFWvWrOH5559n+vTp/Pzzz+WmvPfu3cs//vEPWrZsyQcffECtWrWY\nOnUqY8eOZf78+Rw/fpzevXuX7TJ1zTXXlJ1rt9uZOnUqXbt2ZerUqTzyyCNMmzaN06dPA7Bv3z6a\nN2/OlClT6Nq1K++//77H8yHij1S8Rfzcd999xw033EBkZCRBQUHceOONrFu3ruz7HTp0wGYr/avg\noYceom/fvgDUrl2b+Ph4jh07Vum1jx07RnZ2Nr/73e8AaNasGTVr1mTPnj1AaTOHTp06AdCkSZOy\naXcRuTSaNhfxcwUFBfz73/9m6dKlAJw9e7ZcD+JzzWgA9uzZU3a3bbPZOHny5EVbF+bm5hIVFYVh\nGGXHoqKiyMnJIT4+vtxe2DabDbvd7s4fTSRgqXiL+LmEhAQ6duxIt27dHH52+vTpdO/enVtuuQXD\nMBgwYMBFPx8fH8+pU6cwTbOsgJ86dYq4uDi3xC4iFdO0uYgfCgoKoqCgAIBOnTqxcuVKioqKgNKO\nXStWrKjwvJycHJo2bYphGKxYsYKioiIKCwvLrpmfn1/u8zVr1qRGjRqsXr0aKO0hnZ2dTUpKSjX9\nZCICuvMW8UudO3dm7ty5/PzzzzzwwAMcPHiQ//f//h9Qupb96KOPVnher169mDRpEjExMdx8883c\nfPPNvPLKK0yYMIEuXbowdepUevXqVfZ5wzAYOnQor732Gu+99x5hYWEMGzaM8PBwj/ycIoFKLUFF\nRER8jKbNRUREfIyKt4iIiI9R8RYREfExKt4iIiI+RsVbRETEx6h4i4iI+BgVbxERER+j4i0iIuJj\nVLxFRER8zP8HSGFsPkacIj4AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 576x396 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.ylabel('Number of inferred clusters')\n",
        "plt.xlabel('Iteration')\n",
        "plt.yticks(np.arange(1, max(estimated_num_of_clusters) + 1, 1))\n",
        "plt.plot(iterations - 1, estimated_num_of_clusters)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o4xYcGOI6tQX"
      },
      "source": [
        "Over the iterations, the number of clusters is getting closer to three. With the result of convergence of $\\alpha$ to smaller value over iterations, we can see the model is successfully learning the parameters to infer an optimal number of clusters.\n",
        "\n",
        "Interestingly, we can see the inference has already converged to the correct number of clusters in the early iterations, unlike $\\alpha$ converged in much later iterations. \n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QRw1QyCmOYKv"
      },
      "source": [
        "### 4.7. Fitting the model using RMSProp "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MXI8sY_goqxb"
      },
      "source": [
        "In this section, to see the effectiveness of Monte Carlo sampling scheme of pSGLD, we use RMSProp to fit the model. We choose RMSProp for comparison because it comes without the sampling scheme and pSGLD is based on RMSProp.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Flu4BWaFqs1b"
      },
      "outputs": [],
      "source": [
        "# Learning rates and decay\n",
        "starter_learning_rate_rmsprop = 1e-2\n",
        "end_learning_rate_rmsprop = 1e-4\n",
        "decay_steps_rmsprop = 1e4\n",
        "\n",
        "# Number of training steps\n",
        "training_steps_rmsprop = 50000\n",
        "\n",
        "# Mini-batch size\n",
        "batch_size_rmsprop = 20"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "2evhcErL8TqK"
      },
      "outputs": [],
      "source": [
        "# Define trainable variables.\n",
        "mix_probs_rmsprop = tf.nn.softmax(\n",
        "    tf.Variable(\n",
        "        name='mix_probs_rmsprop',\n",
        "        initial_value=np.ones([max_cluster_num], dtype) / max_cluster_num))\n",
        "\n",
        "loc_rmsprop = tf.Variable(\n",
        "    name='loc_rmsprop',\n",
        "    initial_value=np.zeros([max_cluster_num, dims], dtype)\n",
        "    + np.random.uniform(\n",
        "        low=-9, #set around minimum value of sample value\n",
        "        high=9, #set around maximum value of sample value\n",
        "        size=[max_cluster_num, dims]))\n",
        "\n",
        "precision_rmsprop = tf.nn.softplus(tf.Variable(\n",
        "    name='precision_rmsprop',\n",
        "    initial_value=\n",
        "    np.ones([max_cluster_num, dims], dtype=dtype)))\n",
        "\n",
        "alpha_rmsprop = tf.nn.softplus(tf.Variable(\n",
        "    name='alpha_rmsprop',\n",
        "    initial_value=\n",
        "    np.ones([1], dtype=dtype)))\n",
        "\n",
        "training_vals_rmsprop =\\\n",
        "    [mix_probs_rmsprop, alpha_rmsprop, loc_rmsprop, precision_rmsprop]\n",
        "\n",
        "# Prior distributions of the training variables\n",
        "\n",
        "#Use symmetric Dirichlet prior as finite approximation of Dirichlet process.\n",
        "rv_symmetric_dirichlet_process_rmsprop = tfd.Dirichlet(\n",
        "    concentration=np.ones(max_cluster_num, dtype)\n",
        "    * alpha_rmsprop / max_cluster_num,\n",
        "    name='rv_sdp_rmsprop')\n",
        "\n",
        "rv_loc_rmsprop = tfd.Independent(\n",
        "    tfd.Normal(\n",
        "        loc=tf.zeros([max_cluster_num, dims], dtype=dtype),\n",
        "        scale=tf.ones([max_cluster_num, dims], dtype=dtype)),\n",
        "    reinterpreted_batch_ndims=1,\n",
        "    name='rv_loc_rmsprop')\n",
        "\n",
        "\n",
        "rv_precision_rmsprop = tfd.Independent(\n",
        "    tfd.InverseGamma(\n",
        "        concentration=np.ones([max_cluster_num, dims], dtype),\n",
        "        rate=np.ones([max_cluster_num, dims], dtype)),\n",
        "    reinterpreted_batch_ndims=1,\n",
        "    name='rv_precision_rmsprop')\n",
        "\n",
        "rv_alpha_rmsprop = tfd.InverseGamma(\n",
        "    concentration=np.ones([1], dtype=dtype),\n",
        "    rate=np.ones([1]),\n",
        "    name='rv_alpha_rmsprop')\n",
        "\n",
        "# Define mixture model\n",
        "rv_observations_rmsprop = tfd.MixtureSameFamily(\n",
        "    mixture_distribution=tfd.Categorical(probs=mix_probs_rmsprop),\n",
        "    components_distribution=tfd.MultivariateNormalDiag(\n",
        "        loc=loc_rmsprop,\n",
        "        scale_diag=precision_rmsprop))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "oLyOUVlRrEVe"
      },
      "outputs": [],
      "source": [
        "og_prob_parts_rmsprop = [\n",
        "    rv_loc_rmsprop.log_prob(loc_rmsprop),\n",
        "    rv_precision_rmsprop.log_prob(precision_rmsprop),\n",
        "    rv_alpha_rmsprop.log_prob(alpha_rmsprop),\n",
        "    rv_symmetric_dirichlet_process_rmsprop\n",
        "        .log_prob(mix_probs_rmsprop)[..., tf.newaxis],\n",
        "    rv_observations_rmsprop.log_prob(observations_tensor)\n",
        "    * num_samples / batch_size\n",
        "]\n",
        "joint_log_prob_rmsprop = tf.reduce_sum(\n",
        "    tf.concat(log_prob_parts_rmsprop, axis=-1), axis=-1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "U2BJmk6crzMz"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "RMSProp elapsed_time: 53.7574200630188 seconds (50000 iterations)\n",
            "pSGLD elapsed_time: 309.8013095855713 seconds (10000 iterations)\n"
          ]
        }
      ],
      "source": [
        "# Define learning rate scheduling\n",
        "global_step_rmsprop = tf.Variable(0, trainable=False)\n",
        "learning_rate = tf.train.polynomial_decay(\n",
        "    starter_learning_rate_rmsprop,\n",
        "    global_step_rmsprop, decay_steps_rmsprop,\n",
        "    end_learning_rate_rmsprop, power=1.)\n",
        "\n",
        "# Set up the optimizer. Don't forget to set data_size=num_samples.\n",
        "optimizer_kernel_rmsprop = tf.train.RMSPropOptimizer(\n",
        "    learning_rate=learning_rate,\n",
        "    decay=0.99)\n",
        "\n",
        "train_op_rmsprop = optimizer_kernel_rmsprop.minimize(-joint_log_prob_rmsprop)\n",
        "\n",
        "init_rmsprop = tf.global_variables_initializer()\n",
        "sess.run(init_rmsprop)\n",
        "\n",
        "start = time.time()\n",
        "for it in range(training_steps_rmsprop):\n",
        "  [\n",
        "      _\n",
        "  ] = sess.run([\n",
        "      train_op_rmsprop\n",
        "  ], feed_dict={\n",
        "      observations_tensor: sess.run(next_batch)})\n",
        "\n",
        "elapsed_time_rmsprop = time.time() - start\n",
        "print(\"RMSProp elapsed_time: {} seconds ({} iterations)\"\n",
        "      .format(elapsed_time_rmsprop, training_steps_rmsprop))\n",
        "print(\"pSGLD elapsed_time: {} seconds ({} iterations)\"\n",
        "      .format(elapsed_time_psgld, training_steps))\n",
        "\n",
        "mix_probs_rmsprop_, alpha_rmsprop_, loc_rmsprop_, precision_rmsprop_ =\\\n",
        "  sess.run(training_vals_rmsprop)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vqxJf_I4szUA"
      },
      "source": [
        "Compare to pSGLD, although the number of iterations for RMSProp is longer, optimization by RMSProp is much faster.\n",
        "\n",
        "Next, we look at the clustering result."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "31qHgBEksvBV"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Number of inferred clusters = 4\n",
            "\n",
            "Number of elements in each cluster = [ 1644 15267 16647 16442]\n",
            "\n"
          ]
        },
        {
          "data": {
            "image/png": 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NOP1OPin+hB7hPVBVFavOSpg5DK/Hi9fvpcheRJ49DxmZMH0Yg6IGISNT7ijH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\nmP8PFNQyV6r4BFQAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 576x396 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "cluster_asgmt_rmsprop = sess.run(tf.argmax(\n",
        "    tf.reduce_mean(posterior, axis=1), axis=1), feed_dict={\n",
        "        loc_for_posterior: loc_rmsprop_[tf.newaxis, :],\n",
        "        precision_for_posterior: precision_rmsprop_[tf.newaxis, :],\n",
        "        mix_probs_for_posterior: mix_probs_rmsprop_[tf.newaxis, :]})\n",
        "\n",
        "idxs, count = np.unique(cluster_asgmt_rmsprop, return_counts=True)\n",
        "\n",
        "print('Number of inferred clusters = {}\\n'.format(len(count)))\n",
        "np.set_printoptions(formatter={'float': '{: 0.3f}'.format})\n",
        "\n",
        "print('Number of elements in each cluster = {}\\n'.format(count))\n",
        "\n",
        "cmap = plt.get_cmap('tab10')\n",
        "plt.scatter(\n",
        "    observations[:, 0], observations[:, 1],\n",
        "    1,\n",
        "    c=cmap(convert_int_elements_to_consecutive_numbers_in(\n",
        "        cluster_asgmt_rmsprop)))\n",
        "plt.axis([-10, 10, -10, 10])\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gxtBImZbSM1A"
      },
      "source": [
        "The number of clusters was not correctly inferred by RMSProp optimization in our experiment. We also look at the mixture weight."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "LHLTESVeh-4Q"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 576x396 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.ylabel('MAP inferece of mixture weight')\n",
        "plt.xlabel('Component')\n",
        "plt.bar(range(0, max_cluster_num), mix_probs_rmsprop_)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hz_6DJ5xia9I"
      },
      "source": [
        "We can see the incorrect number of components have significant mixture weights.\n",
        "\n",
        "Although the optimization takes longer time, pSGLD, which has Monte Carlo sampling scheme, performed better in our experiment."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5xPj4BlqDmz1"
      },
      "source": [
        "## 5. Conclusion"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qh6HglG-DplW"
      },
      "source": [
        "In this notebook, we have described how to cluster a large number of samples as well as to infer the number of clusters simultaneously by fitting a Dirichlet Process Mixture of Gaussian distribution using pSGLD.\n",
        "\n",
        "The experiment has shown the model successfully clustered samples and inferred the correct number of clusters. Also, we have shown the Monte Carlo sampling scheme of pSGLD allows us to visualize uncertainty in the result. Not only clustering the samples but also we have seen the model could infer the correct parameters of mixture components. On the relationship between the parameters and the number of inferred clusters, we have investigated how the model learns the parameter to control the number of effective clusters by visualizing the correlation between convergence of 𝛼 and the number of inferred clusters. Lastly, we have looked at the results of fitting the model using RMSProp. We have seen RMSProp, which is the optimizer without Monte Carlo sampling scheme,  works considerably faster than pSGLD but has produced less accuracy in clustering.\n",
        "\n",
        "Although the toy dataset only had 50,000 samples with only two dimensions, the mini-batch manner optimization used here is scalable for much larger datasets."
      ]
    }
  ],
  "metadata": {
    "accelerator": "TPU",
    "colab": {
      "collapsed_sections": [],
      "name": "Fitting_DPMM_Using_pSGLD.ipynb",
      "toc_visible": true
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}
